Hello and welcome.
I don't know of any way to prevent Finder from writing these files, as it is part of the way the Mac OS works and keeps track of things. I understand your initiative, as I use several USB flash drives myself to go between Macs and PCs. The files really don't take up that much space at all, usually only about the size of a single page Word document in total, and are hidden by default.
My solution is to mount the flash drive in Windows within Parallels, and then delete the MAC files before unmounting it from there. This works well, especially when using the flash drives as a source for audio files in my hi-fi system...so I don't have to see these files in the browser.
C